STUDYING NUCLEAR FISSION RATE FROM THE POINT OF VIEW OF BROWNIAN MOTION

The problem of the nuclear fission rate is studied from the point of view of Brownian motion. The Fokker-Plank equation is solved by means of the rate ei-genvalue method. The viscosity tensors, the inertia coefficients and the temperature are functions of nuclear deformation. Their effects on the fission rate are also stu-died.     

Fokker-Planck方程的数值解

采用扩散模型研究核裂变,需要求解Fokker-Planck方程。本文提出一个数值计算方法-平均隐式差分方法。对具有粘滞性的核体系的有关裂变动力学量,如几率分布、裂变率、断点处的平均动能以及鞍点到断点的平均扩散时间等一系列物理量做了计算,并与适合大粘滞性的Kramers的解析解做了比较。通过与解析解的比较及对归一常数的检验,证明计算结果精确可靠。     

EFFECT OF NUCLEAR VISCOSITY ON FISSION PROCESS

According to the fission diffusion model,the deformation motion of fission nucleues is regarded as a diffusion process of quasi-Brownian particles under fission potential,Through simulating such Brownian motion in two dimensional phase space by Monte-Carlo method,the effect of nuclear viscosity on Brownian particle diffusion is studied,Dynamical quantities,suchas fission rate,kinetic energy distribution on scission,and so on are numerally calculated for various viscosity coefficients,The results are reasonable in physics,This method can be easily extended to deal with multi-dimensional diffusion problems.     

Calculations of Stationary Fission Rate by the Partition Function Method

The stationary nuclear fission rate including both thermodynamic and quantal fluctuations are studied by using the partition function method, which is related to the imaginary part of the free energy by R_f = (2/h)k_BT_cIm In Z (Z is the partition function). We calculate the classical fission rate with a coordinatedependent mass within a onedimensional model. The contributions of'additional degrees of fieedom, angular momentum and viscosity to the quantal fission rate at finite temperature are also discussed. Differences between the two- or three-dimensional and the onedimensional cases are analyzed by using the {c, h, a} parametrization.     

重离子裂变反应动力学研究

从实验角度评述了重离子裂变反应动力学研究现状．内容包括动力学裂变宽度、裂变时标、核粘滞性的温度和形变相关性以及从裂变实验上研究核粘滞性的方法等． The present status of the dynamics study for heavy ion induced fission reaction includesing the dynamical fission width,the fission time scale,the temperature and deformation dependence of the nuclear viscosity and the methods of the extracting viscosity from fission experiments induced by heavy ion reactions is reviewed.      

Manifestation of the nuclear viscosity effects in induced fission reactions at excitation energies below 30 MeV

A large set of experimental observables for the ²³²Th(α, xnf)reaction was analyzed theoretically within the dynamic-statistical approach, making it possible to interconsistently consider the manifestation of nuclear viscosity, the double-humped structure of the fission barrier, and the phenomenon of shell effect damping with temperature. Analyses were performed for the energy dependence of the finite lifetime effect in the investigated reaction, obtained using the crystal blocking technique; the fission probability isotopes produced in this reaction during the development of a neutron emission cascade; and the anisotropy of angular distributions of fission fragments. It is shown that this analysis allows us to obtain information regarding nuclear viscosity and its energy dependence at relatively low excitation energies (<30 MeV).     

Evaporation and fission of hot metallic clusters and hot nuclei

Evaporation and fission of metallic clusters are described by models developed in nuclear physics which are appropriately modified. Results of calculations for evaporation rates, appearance sizes and fission times (with and without viscosity) are presented. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Fission decay widths for heavy-ion fusion-fission reactions

Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state, the temperature dependence of the location of fission transition points, and the orientation degree of freedom. The strong increase in the nuclear viscosity above a temperature of approximately 1 MeV deduced by others is an artifact generated by an inadequate fission model.     

Static viscosity of nuclear matter

The static shear viscosity η₀ of symmetric nuclear matter is estimated. It is found, that for reasonable nuclear temperatures the mean free path connected with η_o is considerably larger than the nuclear radii. We therefore conclude, that the concept of viscosity cannot be applied to nuclear fission and heavy ion collisions without taking into account the nuclear surface.     

THE ESCAPE OF BROWNIAN PARTICLE OVER POTENTIAL BARRIERS

A convenient method is introduced to calculate the rate of escape of Brownian particle over potential barriers by exact solution of Smoluchowskian equation. This method is applied to calculate the nuclear fission probabilities. The results for four different cases are compared with the results of other theories.     

Electromagnetic and nuclear fission of238U in the reaction of 100, 500, and 1000 A·MeV208Pb with238U

The folding- and azimuthal-angle and velocity distributions for the²³⁸U fission fragments have been measured in reactions with 100, 500, and 1000 A·MeV²⁰⁸Pb. These distributions were used to decompose the fission cross section into its electromagnetic and nuclear components. The fraction of electromagnetic fission was found to be 0.16±0.07, 0.48±0.08, and 0.60±0.04, respectively. The electromagnetic fission cross section as a function of the²⁰⁸Pb nucleus energy is compared with theoretical predictions. The measured fission cross section from nuclear reactions (≈1.5 b) is approximately constant between 100 and 1000 A·MeV.     

Catapult mechanism for fast particle emission in fission and heavy ion reactions

The fission process of slabs of nuclear matter is modelled in TDHF approximation by adding an initial collective velocity field to the static self-consistent solution. In dependence on its amplitude either large amplitude density oscillations are excited or fission occurs. The final disintegration of the slab proceeds on a time scale of 10^?22s and is characterized by a sharp peak in the actual velocity field in the region of the “snatching” inner low density tails. A characteristic time later corresponding to the transit time of a nucleon across the fragment with mean velocity being the Fermi velocity plus twice the maximum “snatching” velocity, a low density lump correlated with a peak in the velocity field emerges in front of the fragments. We call these particles “catapult particles”. Recent experimental results possibly provide evidence for catapult neutrons in low-energy fission. We also speculate on the significance of the catapult mechanism for fast particle emission in the exit channel of heavy ion reactions.     

Prompt radiation as a probe for fission dynamics

It is shown that the Strutinsky-Denisov induced polarization mechanism leads to the appearance of the prompt electric dipole radiation from fission fragments of ²³⁵Uby thermal neutrons in the domain of around 5 MeV. The probability of the radiation is at the level of 0.001 per fission, which is in agreement with experiment. The angular distribution exhibits left-right asymmetry with respect to the direction of the neutron polarization axis. That means that the emission of gamma quanta at the given angle depends on the neutron polarization. The asymmetry is at the level of 10⁻³. The study of this effect will give a direct information about the scission configuration, nuclear viscosity, and dissipation properties of the collective energy of the surface vibration in fragments with large amplitude. This will give a complete picture of the process of snapping back the nuclear surface.     

量子非欧姆阻尼环境中的重核熔合概率及热核裂变速率

考虑处于量子非欧姆阻尼环境下的重核熔合及热核裂变系统的动力学,给出了数值模拟相应c数量子广义朗之万方程的方法。其中提出的产生任意关联量子色噪声的数值方法,适用于任意非马尔科夫过程噪声的产生。利用此方法计算了重核熔合概率,结果表明量子涨落对重核熔合具有“低抬高压”的效应:当粒子的初始动能小于（大于）临界初始动能时,量子涨落会增大（减小）粒子鞍点通过概率。非欧姆阻尼环境中粒子稳定通过概率随δ值的变化是非单调的,且当粒子初始动能小于（大于）临界初始动能,量子涨落会使稳定通过概率随δ值变化曲线的极大值位置向右（向左）漂移。此外,在热核裂变系统中,超欧姆阻尼环境会增大裂变速率,而量子涨落不仅显著增大裂变速率,还使裂变速率随δ值变化曲线的极大值位置发生漂移。Dynamics of heavy-ion fusion and nuclear fission system in a quantum non-Ohmic environment have been considered and a numerical simulation method to solve the corresponding c-number quantum generalized Langevin equation is proposed. The method of generating quantum colored noise with arbitrary correlation can be applied to generate noise of arbitrary non-Markov process. Calculating fusion probability of heavy nuclei with this method, the result has shown that the passing probability is enlarged (decreased) by the quantum fluctuation when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Steady passing probability of particle in non-Ohmic environment versus is nonmonotonic. Quantum fluctuation makes the maximum position of the curve drift towards right (left), when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Furthermore, nuclear fission rate is larger in super-Ohmic environment. Quantum fluctuation enlarges nuclear fission rate and makes the the maximum position of nuclear fission rate versus δ drift.     

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

Spin distribution of evaporation residue cross section within a stochastic approach

The Langevin equation including particle emission was used to reproduce the recently measured spin distribution of evaporation residue cross sections in the reaction 16O+184W at beam energies of 84, 92,100, 108, 116 and 120 MeV. By comparing the theoretical calculations with the experimental data, the validity of the stochastic approach to dissipative fission is verified. Moreover, a pre-saddle nuclear viscosity coefficient of 5 x 1021 S-1 is extracted.     

重核熔合与裂变位垒的动力学回流现象

用实验粒子多次通过位垒的方法计算重核熔合与裂变过程中的熔合几率和裂变速率,结果发现位垒附近存在着一种强烈的回流现象.研究还表明当鞍点后势变得平滑,则回流变大.这种效应降低了以往所用的实验粒子首次通过位垒方法得到的熔合几率和裂变速率,从而给出这两种量的正确描述